# A random matrix analysis and improvement of semi-supervised learning for large dimensional data

arXiv: https://arxiv.org/abs/1711.03404 · HTML: https://mlsanity.com/paper/1711.03404/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Nov 2017.

## Built on by (most cited first, 10 of 10)

- [A Random Matrix Perspective on Random Tensors](https://mlsanity.com/paper/2108.00774/) (2021)
- [Two-way kernel matrix puncturing: towards resource-efficient PCA and spectral clustering](https://mlsanity.com/paper/2102.12293/) (2021)
- [Hamilton-Jacobi equations on graphs with applications to semi-supervised learning and data depth](https://mlsanity.com/paper/2202.08789/) (2022)
- [Random Matrix Analysis to Balance between Supervised and Unsupervised Learning under the Low Density Separation Assumption](https://mlsanity.com/paper/2310.13434/) (2023)
- [Consistency of semi-supervised learning, stochastic tug-of-war games, and the p-Laplacian](https://mlsanity.com/paper/2401.07463/) (2024)
- [Persistent Laplacian-enhanced Algorithm for Scarcely Labeled Data Classification](https://mlsanity.com/paper/2305.16239/) (2023)
- [A Large Dimensional Analysis of Multi-task Semi-Supervised Learning](https://mlsanity.com/paper/2402.13646/) (2024)
- [Higher-Order Regularization Learning on Hypergraphs](https://mlsanity.com/paper/2510.26533/) (2025)
- [Asymptotic Bayes risk of semi-supervised learning with uncertain labeling](https://mlsanity.com/paper/2403.17767/) (2024)
- [Interface Laplace Learning: Learnable Interface Term Helps Semi-Supervised Learning](https://mlsanity.com/paper/2408.05419/) (2024)

## Abstract (arXiv)

This article provides an original understanding of the behavior of a class of graph-oriented semi-supervised learning algorithms in the limit of large and numerous data. It is demonstrated that the intuition at the root of these methods collapses in this limit and that, as a result, most of them become inconsistent. Corrective measures and a new data-driven parametrization scheme are proposed along with a theoretical analysis of the asymptotic performances of the resulting approach. A surprisingly close behavior between theoretical performances on Gaussian mixture models and on real datasets is also illustrated throughout the article, thereby suggesting the importance of the proposed analysis for dealing with practical data. As a result, significant performance gains are observed on practical data classification using the proposed parametrization.